14 research outputs found
Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions
In systems involving quantitative data, such as probabilistic, fuzzy, or
metric systems, behavioural distances provide a more fine-grained comparison of
states than two-valued notions of behavioural equivalence or behaviour
inclusion. Like in the two-valued case, the wide variation found in system
types creates a need for generic methods that apply to many system types at
once. Approaches of this kind are emerging within the paradigm of universal
coalgebra, based either on lifting pseudometrics along set functors or on
lifting general real-valued (fuzzy) relations along functors by means of fuzzy
lax extensions. An immediate benefit of the latter is that they allow bounding
behavioural distance by means of fuzzy (bi-)simulations that need not
themselves be hemi- or pseudometrics; this is analogous to classical
simulations and bisimulations, which need not be preorders or equivalence
relations, respectively. The known generic pseudometric liftings, specifically
the generic Kantorovich and Wasserstein liftings, both can be extended to yield
fuzzy lax extensions, using the fact that both are effectively given by a
choice of quantitative modalities. Our central result then shows that in fact
all fuzzy lax extensions are Kantorovich extensions for a suitable set of
quantitative modalities, the so-called Moss modalities. For nonexpansive fuzzy
lax extensions, this allows for the extraction of quantitative modal logics
that characterize behavioural distance, i.e. satisfy a quantitative version of
the Hennessy-Milner theorem; equivalently, we obtain expressiveness of a
quantitative version of Moss' coalgebraic logic. All our results explicitly
hold also for asymmetric distances (hemimetrics), i.e. notions of quantitative
simulation
Characteristic Logics for Behavioural Metrics via Fuzzy Lax Extensions
Behavioural distances provide a fine-grained measure of equivalence in systems involving quantitative data, such as probabilistic, fuzzy, or metric systems. Like in the classical setting of crisp bisimulation-type equivalences, the wide variation found in system types creates a need for generic methods that apply to many system types at once. Approaches of this kind are emerging within the paradigm of universal coalgebra, based either on lifting pseudometrics along set functors or on lifting general real-valued (fuzzy) relations along functors by means of fuzzy lax extensions. An immediate benefit of the latter is that they allow bounding behavioural distance by means of fuzzy bisimulations that need not themselves be (pseudo-)metrics, in analogy to classical bisimulations (which need not be equivalence relations). The known instances of generic pseudometric liftings, specifically the generic Kantorovich and Wasserstein liftings, both can be extended to yield fuzzy lax extensions, using the fact that both are effectively given by a choice of quantitative modalities. Our central result then shows that in fact all fuzzy lax extensions are Kantorovich extensions for a suitable set of quantitative modalities, the so-called Moss modalities. For non-expansive fuzzy lax extensions, this allows for the extraction of quantitative modal logics that characterize behavioural distance, i.e. satisfy a quantitative version of the Hennessy-Milner theorem; equivalently, we obtain expressiveness of a quantitative version of Moss\u27 coalgebraic logic
Logic and Commonsense Reasoning: Lecture Notes
MasterThese are the lecture notes of a course on logic and commonsense reasoning given to master students in philosophy of the University of Rennes 1. N.B.: Some parts of these lectures notes are sometimes largely based on or copied verbatim from publications of other authors. When this is the case, these parts are mentioned at the end of each chapter in the section “Further reading”
Modelling causal reasoning
PhDAlthough human causal reasoning is widely acknowledged as an object
of scientific enquiry, there is little consensus on an appropriate measure
of progress. Up-to-date evidence of the standard method of research in
the field shows that this method has been rejected at the birth of modern
science.
We describe an instance of the standard scientific method for modelling
causal reasoning (causal calculators). The method allows for uniform
proofs of three relevant computational properties: correctness of the model
with respect to the intended model, full abstraction of the model (function)
with respect to the equivalence of reasoning scenarios (input), and formal
relations of equivalence and subsumption between models. The method
extends and exploits the systematic paradigm [Handbook of Logic in Artificial
Intelligence and Logic Programming, volume IV, p. 439-498, Oxford 1995] to
fit with our interpretation of it.
Using the described method, we present results for some major models,
with an updated summary spanning seventy-two years of research in the
field
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Proceedings of The Multi-Agent Logics, Languages, and Organisations Federated Workshops (MALLOW 2010)
http://ceur-ws.org/Vol-627/allproceedings.pdfInternational audienceMALLOW-2010 is a third edition of a series initiated in 2007 in Durham, and pursued in 2009 in Turin. The objective, as initially stated, is to "provide a venue where: the cost of participation was minimum; participants were able to attend various workshops, so fostering collaboration and cross-fertilization; there was a friendly atmosphere and plenty of time for networking, by maximizing the time participants spent together"